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A154747 Decimal expansion of sqrt(sqrt(2) - 1), the radius vector of the point of bisection of the arc of the unit lemniscate (x^2 + y^2)^2 = x^2 - y^2 in the first quadrant. 7
6, 4, 3, 5, 9, 4, 2, 5, 2, 9, 0, 5, 5, 8, 2, 6, 2, 4, 7, 3, 5, 4, 4, 3, 4, 3, 7, 4, 1, 8, 2, 0, 9, 8, 0, 8, 9, 2, 4, 2, 0, 2, 7, 4, 2, 4, 4, 4, 0, 0, 7, 6, 5, 1, 1, 5, 6, 1, 5, 2, 0, 0, 9, 3, 5, 2, 0, 7, 4, 8, 5, 0, 3, 2, 1, 8, 3, 6, 5, 1, 9, 5, 4, 5, 1, 3, 4, 2, 4, 6, 5, 9, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

A root of r^4 + 2 r^2 - 1 = 0.

Also real part of sqrt(1 + i)^3, where i is the imaginary unit such that i^2 = -1. - Alonso del Arte, Sep 09 2019

REFERENCES

C. L. Siegel, Topics in Complex Function Theory, Volume I: Elliptic Functions and Uniformization Theory, Wiley-Interscience, 1969, page 5

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

EXAMPLE

0.643594252905582624735443437418...

MATHEMATICA

nmax = 1000; First[ RealDigits[ Sqrt[Sqrt[2] - 1], 10, nmax] ]

PROG

(PARI) sqrt(sqrt(2) - 1) \\ Michel Marcus, Dec 10 2016

CROSSREFS

Cf. A154739 for the abscissa and A154743 for the ordinate.

Cf. A154748, A154749 and A154750 for the continued fraction and the numerators and denominators of the convergents.

Cf. A085565 for 1.311028777..., the first-quadrant arc length of the unit lemniscate.

Cf. A309948 and A309949 for real and imaginary parts of sqrt(1 + i).

Sequence in context: A235509 A224927 A200104 * A217515 A079624 A035335

Adjacent sequences:  A154744 A154745 A154746 * A154748 A154749 A154750

KEYWORD

nonn,cons,easy

AUTHOR

Stuart Clary, Jan 14 2009

EXTENSIONS

Offset corrected by R. J. Mathar, Feb 05 2009

STATUS

approved

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Last modified May 27 05:48 EDT 2020. Contains 334649 sequences. (Running on oeis4.)